Answer:
The answer to your question is
a) 400
b) The function has two real solutions (-2 and 8)
Step-by-step explanation:
Process
1.- Discriminant = b² - 4ac
= 12² -4(-2)(32)
= 144 + 256
= 400
2.- Solutions (using the general formula)
x = [tex]\frac{- b +/- \sqrt{b^{2}- 4ac}}{2a}[/tex]
x = [tex]\frac{- 12 +/- \sqrt{400}}{2(-2)}[/tex]
x = [tex]\frac{-12 +/- 20}{2(-2)}[/tex]
x₁ = [tex]\frac{-12 + 20}{2(-2)} = \frac{-12 + 20}{-4} = \frac{-8}{4} = - 2[/tex]
x₂ = [tex]\frac{- 12 - 20}{- 4} = \frac{-32}{- 4} = 8[/tex]
This function has two real solutions (-2, 8)
